Problem:
A vector space V
Please help with the following problem.
Please be as professional and as clear as possible in your response. Pay close attention to instructions.
Determine if the set R^2 (the real plane) is a vector space with operations defined by the following:
Addition: (a,b)+(c,d)=(a+c,b+d)
Scalar Multiplication: k(a,b)=(0,0)
Prove your answer. If this structure is not a vector space, state all the axioms of a vector space which are not satisfied and explain your answer.